Consider a PIB with a sloped bottom. You want to try perturbation

Slides:

Advertisements

Similar presentations

Advertisements

Bohr Model of the Hydrogen Atom Postulates Certain orbits are stationary. Photon emission occurs upon orbital trans. Angular momentum is quantized.

Consider the He atom. It has 2 electrons, each with its own spin, and. Adding spin angular momenta means adding vectors. With this in mind, what are the.

Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel.

Physics 452 Quantum mechanics II Winter 2011 Karine Chesnel.

Lecture 22 Spin-orbit coupling

Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel.

Quantum Numbers Activity. Quantum Numbers Quantum numbers tell us properties of the atomic orbitals, and electrons, in an atom. Like giving each electron.

Orbitals and Quantum Numbers. Objective Students will be able to describe the quantum numbers n, l, and m l used to define an orbital in an atom, and.

Bohr Model Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. After lots of math,

Hydrogen Atom – Atomic Orbitals Lecture - 3 X Y Z x P (e - ) z Q y R.

An Electron Trapped in A Potential Well Probability densities for an infinite well Solve Schrödinger equation outside the well.

6.852: Distributed Algorithms Spring, 2008 April 1, 2008 Class 14 – Part 2 Applications of Distributed Algorithms to Diverse Fields.

Slide 1/21 CHEM2915 A/Prof Adam Bridgeman Room: Introduction to the Electronic.

ELECTROMAGNETIC SPECTRUM. OUTER (VALENCE) ELECTRONS AND ATOMIC STRUCTURE U.V. and VISIBLEOuter Valence Electrons in Atoms & Molecules Give Rise to Atomic.

Arrangement of Electrons in Atoms

Electronic States of Atoms Quantum numbers for electronsQuantum numbers for many-electron atoms l: orbital angular momentum quantumL: orbital angular.

Physics 541 A quantum approach to condensed matter physics.

Atomic Orbitals And Quantum Numbers. Quantum Numbers A series of 4 numbers (and/or letters) that specify the properties of an electron in its orbit The.

Lecture 22 Spin-orbit coupling. Spin-orbit coupling Spin makes an electron act like a small magnet. An electron orbiting around the nucleus also makes.

Quantum Numbers n, l, m, and s – Used to describe an electron in an atom Probable location n – Principal Quantum Number – Represents main energy level.

Atomic Physics Quantum Physics 2002 Recommended Reading: Harris Chapter 7.

Lecture 21 More on singlet and triplet helium (c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign. This material has been.

4.2b Quantum Numbers and Atomic Orbitals. POINT > Describe the Principle Quantum number as an energy level POINT > Calculate number of electrons at different.

Physics 1202: Lecture 34 Today’s Agenda Announcements: Extra creditsExtra credits –Final-like problems –Team in class –Teams 5 & 6 HW 10 due FridayHW 10.

CHAPTER 7: Review The Hydrogen Atom

Quantums numbers & the probability of where an electron may be found

Last hour: Generalized angular momentum EV’s: j·(j+1)·ħ2 for ; m·ħ for ; -j ≤ m ≤ j in steps of 1 The quantum numbers j can be.

Quantum Theory and the Atom

Perturbation Theory Lecture 2 Books Recommended:

Orbitals and Quantum Numbers

4.2b Quantum Numbers and Atomic Orbitals

Homework # 10 Worksheet: Quantum Numbers

 Heisenberg’s Matrix Mechanics Schrödinger’s Wave Mechanics

4.7 – NOTES Intro to Electron Configurations

Perturbation Theory Lecture 2 continue Books Recommended:

Quantum mechanics I Fall 2012

Electronic Structure of Atoms

Spin and Magnetic Moments

Consider the effective potential

The Quantum Model of the Atom.

Quantum Theory Light Theory Part 4.

WARM UP Name 3 scientists who worked on quantum theory or quantum mechanics. Describe their contribution in 3 words or less.

Quantum Theory and Electronic Structure of the Atom

Quantum Mechanical View of Atoms

QM2 Concept Test 2.1 Which one of the following pictures represents the surface of constant

Will the orbital energies for multielectron atoms depend on their angular momentum quantum number ℓ? (A) In the H atom, the orbital energies depend on.

Lecture 21 More on singlet and triplet helium

Consider the He atom. The Hamiltonian is

Chapter 4 Electrons as Waves

Bound Systems and Spectra

Quantum Mechanics.

Quantum Numbers Activity

Consider the He atom. It has 2 electrons, each with its own spin,

Multielectron Atoms The quantum mechanics approach for treating multielectrom atoms is one of successive approximations The first approximation is to treat.

Chemistry Department of Fudan University

QM1 Concept test 1.1 Consider an ensemble of hydrogen atoms all in the ground state. Choose all of the following statements that are correct. If you make.

Solutions () to Schrodinger’s Equation

Pauli Principle: The total WF must be antisymmetric w. r

How does the probability density

Group theory and intrinsic spin; specifically, s=1/2

Quantum Numbers.

“Addition” of angular momenta – Chap. 15

QM2 Concept Test 11.1 In a 3D Hilbert space,

PHY 741 Quantum Mechanics 12-12:50 AM MWF Olin 103

Addition of Angular Momentum

Quantum Theory Electrons!.

The Bohr Model, Wave Model, and Quantum Model

The Quantum-Mechanical Hydrogen Atom

Quantum Theory and the Electronic Structure of Atoms

Presentation transcript:

Consider a PIB with a sloped bottom. You want to try perturbation V(x) Consider a PIB with a sloped bottom. You want to try perturbation theory to solve this problem. How do you choose the perturbation Hamiltonian? (A) (B) (C) x

Consider a PIB with a sloped bottom. You want to try perturbation V(x) Consider a PIB with a sloped bottom. You want to try perturbation theory to solve this problem. How do you choose the perturbation Hamiltonian? (A) (B) (C) x

Consider the He atom. The Hamiltonian is What is the perturbation Hamiltonian? (A) (B) (C) (D)

Consider the He atom. The Hamiltonian is What is the perturbation Hamiltonian? (A) (B) (C) (D)

If we neglect the electron-electron interaction, the total wave function of the He atom in the ground state is ... (A) ... the sum of two 1s electron wave functions (B) ... the difference of two 1s electron wave functions (C) ... the product of two 1s electron wave functions

If we neglect the electron-electron interaction, the total wave function of the He atom in the ground state is ... (A) ... the sum of two 1s electron wave functions won’t be normalized any more! (B) ... the difference of two 1s electron wave functions (C) ... the product of two 1s electron wave functions ||2 correctly describes probability density as |(1)|2 |(2)|2

What is electron spin? (A) It’s the same as the orbital angular momentum of the electron. (B) It’s a form of angular momentum, but it is described by half-integer quantum numbers. (C) It’s just another form of angular momentum, adding 1/2ħ to the orbital angular momentum. (D) It’s another form of angular momentum with quantum numbers going from s = 0 to s = ℓ. (E) It’s another form of angular momentum with possible quantum numbers s = 1 and s = 3 (singlet and triplet states).

What is electron spin? (A) It’s the same as the orbital angular momentum of the electron. (B) It’s a form of angular momentum, but it is described by half -integer quantum numbers. (C) It’s just another form of angular momentum, adding 1/2ħ to the orbital angular momentum. (D) It’s another form of angular momentum with quantum numbers going from s = 0 to s = ℓ. (E) It’s another form of angular momentum with possible quantum numbers s = 1 and s = 3 (singlet and triplet states).